# Load necessary libraries
library(dplyr)
##
## Attaching package: 'dplyr'
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## filter, lag
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library(tidyr)
library(ggplot2)
library(bipartite) # For network analysis
## Warning: package 'bipartite' was built under R version 4.3.3
## Loading required package: vegan
## Warning: package 'vegan' was built under R version 4.3.3
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## Loading required package: sna
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## Loading required package: network
##
## 'network' 1.18.2 (2023-12-04), part of the Statnet Project
## * 'news(package="network")' for changes since last version
## * 'citation("network")' for citation information
## * 'https://statnet.org' for help, support, and other information
## sna: Tools for Social Network Analysis
## Version 2.8 created on 2024-09-07.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
## For citation information, type citation("sna").
## Type help(package="sna") to get started.
## This is bipartite 2.20.
## For latest changes see versionlog in ?"bipartite-package". For citation see: citation("bipartite").
## Have a nice time plotting and analysing two-mode networks.
##
## Attaching package: 'bipartite'
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library(vegan)
library(tibble)
library(lubridate)
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library(igraph)
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library(parallel)
library(foreach)
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library(doParallel)
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## Loading required package: iterators
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library(sf)
## Warning: package 'sf' was built under R version 4.3.3
## Linking to GEOS 3.13.0, GDAL 3.8.5, PROJ 9.5.1; sf_use_s2() is TRUE
library(rnaturalearth)
library(rnaturalearthdata)
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library(geosphere)
## Warning: package 'geosphere' was built under R version 4.3.3
library(readr)
# Read the data
# Read CSV with network_id as character
interactions <- read_csv("Interaction_data.csv",
col_types = cols(
Network_id = col_character()
))
# Summarize network-level information
network_summary <- interactions %>%
group_by(Study_id,Network_id, Country, Bioregion, EuPPollNet_habitat) %>%
summarise(
n_plants = n_distinct(Plant_original_name),
n_pollinators = n_distinct(Pollinator_original_name),
.groups = "drop"
)
# Inspect result
head(network_summary)
## # A tibble: 6 × 7
## Study_id Network_id Country Bioregion EuPPollNet_habitat n_plants
## <chr> <chr> <chr> <chr> <chr> <int>
## 1 10_Vanbergen FR_V02 France Continental Agricultural land 6
## 2 10_Vanbergen FR_V02 France Continental Intensive grasslands 2
## 3 10_Vanbergen FR_V03 France Continental Agricultural land 7
## 4 10_Vanbergen FR_V03 France Continental Forest/woodland 16
## 5 10_Vanbergen FR_V03 France Continental Intensive grasslands 1
## 6 10_Vanbergen FR_V03 France Continental Riparian vegetation 3
## # ℹ 1 more variable: n_pollinators <int>
# Number of unique networks
n_networks <- network_summary %>%
distinct(Network_id, Study_id) %>%
count()
print(n_networks)
## # A tibble: 1 × 1
## n
## <int>
## 1 1630
# Years of data
# Convert to proper Date type
interactions$Date <- as.Date(interactions$Date)
# Extract year and month
interactions <- interactions %>%
mutate(Year = year(Date),
Month = month(Date, label = TRUE, abbr = TRUE)) # e.g. "Jan", "Feb"
networks_per_year <- interactions %>%
distinct(Network_id, Year) %>%
count(Year)
ggplot(networks_per_year, aes(x = Year, y = n)) +
geom_col(fill = "steelblue") +
theme_minimal() +
labs(title = "Temporal coverage of networks",
x = "Year", y = "Number of networks")

# Count distinct studies in each country
studies_per_country <- network_summary %>%
distinct(Study_id, Country) %>%
count(Country, name = "Num_studies")
print(studies_per_country)
## # A tibble: 23 × 2
## Country Num_studies
## <chr> <int>
## 1 Austria 1
## 2 Belgium 1
## 3 Bulgaria 1
## 4 Czech Republic 4
## 5 Denmark 1
## 6 England 1
## 7 Estonia 2
## 8 Finland 1
## 9 France 3
## 10 Germany 9
## # ℹ 13 more rows
# Plot
ggplot(studies_per_country, aes(x = reorder(Country, -Num_studies), y = Num_studies)) +
geom_col(fill = "darkseagreen") +
theme_minimal() +
labs(title = "Number of Studies per Country",
x = "Country", y = "Number of Studies") +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
scale_y_continuous(breaks = seq(0, max(studies_per_country$Num_studies), by = 2))

# Interactions per network
inter_per_net <- interactions %>%
group_by(Network_id) %>%
summarise(Total_Interactions = sum(Interaction)) %>%
arrange(desc(Total_Interactions))
# Get unique Network_id - Bio-region pairs
region_per_net <- interactions %>%
select(Network_id, Bioregion) %>%
distinct()
# Join with interaction summary
inter_per_net_with_region <- inter_per_net %>%
left_join(region_per_net, by = "Network_id")
# Count networks per bio-region
networks_per_bioregion <- network_summary %>%
select(Network_id, Bioregion) %>%
distinct() %>%
count(Bioregion)
# Plot
ggplot(networks_per_bioregion, aes(x = reorder(Bioregion, -n), y = n)) +
geom_bar(stat = "identity", fill = "skyblue") +
labs(title = "Number of Networks per Bioregion",
x = "Bioregion", y = "Number of Networks") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))

# Count networks per country
networks_per_country <- network_summary %>%
select(Network_id, Country) %>%
distinct() %>%
count(Country)
# Plot count of networks per country
ggplot(networks_per_country, aes(x = reorder(Country, -n), y = n)) +
geom_bar(stat = "identity", fill = "steelblue") +
labs(title = "Number of Networks per Country",
x = "Country", y = "Number of Networks") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))

# Get unique network country bio-region combinations
country_bioregion <- network_summary %>%
select(Network_id, Country, Bioregion) %>%
distinct()
# Count networks per country and attach bior-egion
networks_per_country <- country_bioregion %>%
distinct(Network_id, Country, Bioregion) %>%
count(Country, Bioregion)
# Plot
ggplot(networks_per_country, aes(x = reorder(Country, -n), y = n, fill = Bioregion)) +
geom_bar(stat = "identity") +
labs(title = "Number of Networks per Country (Colored by Bioregion)",
x = "Country", y = "Number of Networks") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
scale_fill_brewer(palette = "Set2")

#---- Interactions analysis ----
# Create interaction matrix: rows = networks, columns = species
#pollinators
mat_pollinators <- interactions %>%
select(Network_id, Pollinator_accepted_name) %>%
distinct() %>%
mutate(present = 1) %>%
pivot_wider(names_from = Pollinator_accepted_name, values_from = present, values_fill = 0) %>%
column_to_rownames("Network_id") %>%
as.matrix()
#plants
mat_plants <- interactions %>%
select(Network_id, Plant_accepted_name) %>%
distinct() %>%
mutate(present = 1) %>%
pivot_wider(names_from = Plant_accepted_name, values_from = present, values_fill = 0) %>%
column_to_rownames("Network_id") %>%
as.matrix()
#Pollinators & plants
# Create interaction matrix: rows = plants species, columns = pollinators species
mat_plant_x_poll <- interactions %>%
select(Plant_accepted_name, Pollinator_accepted_name) %>%
distinct() %>%
mutate(present = 1L) %>%
pivot_wider(names_from = Pollinator_accepted_name,
values_from = present, values_fill = 0) %>%
column_to_rownames("Plant_accepted_name") %>%
as.matrix()
# Accumulation curves
# accumulation curve for pollinators
spec_curve <- specaccum(mat_pollinators, method = "random")
df_curve <- data.frame(
Sites = spec_curve$sites,
Richness = spec_curve$richness,
SD = spec_curve$sd
)
# graphing
ggplot(df_curve, aes(x = Sites, y = Richness)) +
geom_line(color = "black", size = 1.2) +
geom_ribbon(aes(ymin = Richness - SD, ymax = Richness + SD),
fill = "grey", alpha = 0.5) +
geom_line(data = df_curve, aes(x = Sites, y = Richness))+
labs(x = "Networks", y = "Pollinator species",
title = "Pollinator Accumulation Curve") +
theme_minimal(base_size = 14)
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# accumulation curve for plants
spec_curve_plants <- specaccum(mat_plants, method = "random")
df_curve_plants <- data.frame(
Sites = spec_curve_plants$sites,
Richness = spec_curve_plants$richness,
SD = spec_curve_plants$sd
)
# graphing
ggplot(df_curve_plants, aes(x = Sites, y = Richness)) +
geom_line(color = "black", size = 1.2) +
geom_ribbon(aes(ymin = Richness - SD, ymax = Richness + SD),
fill = "grey", alpha = 0.5) +
geom_line(data = df_curve_plants, aes(x = Sites, y = Richness))+
labs(x = "Networks", y = "Plants species",
title = "Plants Accumulation Curve") +
theme_minimal(base_size = 14)

# accumulation curve for plants and pollinators
spec_curve_d <- specaccum(mat_plant_x_poll, method = "random", permutations = 200)
df_d <- data.frame(
Plants = spec_curve_d$sites,
Pollinators = spec_curve_d$richness,
SD = spec_curve_d$sd
)
#graphing
ggplot(df_d, aes(x = Plants, y = Pollinators)) +
geom_ribbon(aes(ymin = Pollinators - SD, ymax = Pollinators + SD),
fill = "grey", alpha = 0.5) +
geom_line(color = "black", size = 1.2) +
labs(x = "Plant species", y = "Pollinator species",
title = "Aaccumulation curve of Pollinator across Plant") +
theme_minimal(base_size = 14)

#---- Species distribution ----
# Calculate occurrence proportion for each pollinator
poll_occurrence <- interactions %>%
select(Network_id, Pollinator_accepted_name) %>%
distinct() %>%
count(Pollinator_accepted_name) %>%
mutate(freq = n / n_distinct(interactions$Network_id)) %>%
arrange(desc(freq)) %>%
mutate(rank = row_number())
# Plots
ggplot(poll_occurrence, aes(x = n)) +
geom_histogram(binwidth = 1, color = "purple") +
labs(title = "Distribution of Number of Networks per Number of Pollinators",
x = "Number of networks",
y = "Number of pollinator species") +
theme_minimal()

ggplot(poll_occurrence, aes(x = freq)) +
geom_histogram(binwidth = 0.05, fill = "purple", color = "black") +
labs(title = "Distribution of Pollinator Frequencies",
x = "Frequency across networks",
y = "Number of species") +
theme_minimal()

# # Top pollinators by number of networks
# top_pollinators <- poll_occurrence %>%
# arrange(desc(n)) %>%
# head(70) # change 10 to however many top species you want
#
# # Join with metadata about networks
# top_poll_networks <- interactions %>% # replace with your full data frame
# filter(Pollinator_accepted_name %in% top_pollinators$pollinator) %>%
# distinct(Pollinator_accepted_name, Network_id, Country)
#
# ggplot(top_pollinators, aes(x = reorder(Pollinator_accepted_name, n), y = n)) +
# geom_col(fill = "darkgreen") +
# coord_flip() +
# labs(title = "Top Shared Pollinators Across Networks",
# x = "Pollinator species", y = "Number of networks") +
# theme_minimal()
# Calculate occurrence proportion for each plant
plant_occurrence <- interactions %>%
select(Network_id, Plant_accepted_name) %>%
distinct() %>%
count(Plant_accepted_name) %>%
mutate(freq = n / n_distinct(interactions$Network_id)) %>%
arrange(desc(freq)) %>%
mutate(rank = row_number())
# Plot
ggplot(plant_occurrence, aes(x = n)) +
geom_histogram(binwidth = 1, color = "seagreen") +
labs(title = "Distribution of Number of Networks per Number of Plants",
x = "Number of networks",
y = "Number of Plants species") +
theme_minimal()

ggplot(plant_occurrence, aes(x = freq)) +
geom_histogram(binwidth = 0.05, fill = "seagreen", color = "black") +
labs(title = "Distribution of Plants Frequencies",
x = "Frequency across networks",
y = "Number of species") +
theme_minimal()

#---- Habitats ----
# Count unique networks per habitat
habitat_counts <- network_summary %>%
select(Network_id, EuPPollNet_habitat) %>%
distinct() %>%
count(EuPPollNet_habitat, name = "Num_networks")
# Plot
ggplot(habitat_counts, aes(x = reorder(EuPPollNet_habitat, Num_networks), y = Num_networks)) +
geom_bar(stat = "identity", fill = "skyblue") +
coord_flip() +
labs(title = "Number of Networks per Habitat",
x = "Habitat", y = "Number of Networks") +
theme_minimal()

# Habitats per country
habitat_country_counts <- network_summary %>%
select(Network_id, EuPPollNet_habitat, Country) %>%
distinct() %>%
count(EuPPollNet_habitat, Country)
ggplot(habitat_country_counts, aes(x = reorder(EuPPollNet_habitat, -n), y = n, fill = Country)) +
geom_bar(stat = "identity") +
coord_flip() +
labs(title = "Networks per Habitat and Country",
x = "Habitat", y = "Number of Networks") +
theme_minimal()

ggplot(habitat_country_counts, aes(x = reorder(EuPPollNet_habitat, -n), y = n)) +
geom_bar(stat = "identity", fill = "darkseagreen") +
coord_flip() +
facet_wrap(~ Country, scales = "free_x") +
labs(title = "Networks per Habitat by Country",
x = "Habitat", y = "Number of Networks") +
theme_minimal(base_size = 6)

#-- bioregion ----
# Summarize key metrics by bioregion
bioregion_summary <- network_summary %>%
group_by(Bioregion) %>%
summarise(
Num_Networks = n_distinct(Network_id),
Avg_Plants = mean(n_plants, na.rm = TRUE),
Avg_Pollinators = mean(n_pollinators, na.rm = TRUE),
Total_Interactions = sum(inter_per_net$Total_Interactions[match(Network_id, inter_per_net$Network_id)], na.rm = TRUE),
.groups = "drop"
)
# ---summarizing species per habitat and pollinator order----
#---- Network Analysis ----
# net_species_counts <- network_summary %>%
# select(Network_id, Plant_accepted_name, Pollinator_accepted_name) %>%
# distinct() %>%
# group_by(Network_id) %>%
# summarise(
# N_plants = n_distinct(Plant_accepted_name),
# N_pollinators = n_distinct(Pollinator_accepted_name),
# .groups = "drop"
# )
# Plot geom point graph for the number pf plants an dpollinators
ggplot(network_summary, aes(x = n_plants, y = n_pollinators)) +
geom_point(alpha = 0.6, color = "darkblue") +
labs(title = "Network Size: Number of Species per Network",
x = "Number of Plant Species", y = "Number of Pollinator Species") +
theme_minimal()

# Plot geom point graph for the number of plants and pollinators with bioregion colors
ggplot(network_summary, aes(x = n_plants, y = n_pollinators, color = Bioregion)) +
geom_point(alpha = 0.6, size = 2) +
labs(title = "Number of Species per Network",
x = "Number of Plant Species",
y = "Number of Pollinator Species",
color = "Bioregion") +
theme_minimal() +
theme(legend.position = "right") +
scale_color_brewer(palette = "Set2") # Or use scale_color_viridis_d() for more colors

# Filter and plot large networks (e.g., N_plants and N_pollinators >= 10, adjust threshold as needed)
large_net_threshold <- 30 # Define threshold for "large" networks
large_net_counts <- network_summary %>%
filter(n_plants >= large_net_threshold & n_pollinators >= large_net_threshold)
# # Join with country information
# large_net_with_country <- large_net_counts %>%
# inner_join(interactions %>% distinct(Network_id), by = "Network_id")
ggplot(large_net_counts, aes(x = n_plants, y = n_pollinators, color = Country)) +
geom_point(alpha = 0.6, size = 3) + # Increased size to 3 (adjust as needed)
labs(title = paste0("Large Networks (≥ ", large_net_threshold, " Species)"),
x = "Number of Plant Species", y = "Number of Pollinator Species") +
theme_minimal() +
theme(legend.position = "right") # Adjust legend position as needed

# Summaries total interaction count per network and country
net_interactions_country <- interactions %>%
group_by(Network_id, Country) %>%
summarise(Total_interactions = sum(Interaction), .groups = "drop")
# Plot boxplot of interaction counts by country
ggplot(net_interactions_country, aes(x = Country, y = Total_interactions)) +
geom_boxplot(fill = "lightblue") +
labs(title = "Number of Interactions per Network by Country",
x = "Country", y = "Total Number of Interactions") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))

# For indexes calculations
# Create presence column (1 = presents)
interactions$present <- ifelse(interactions$Interaction > 0, 1, 0)
# Create a named list of matrices (one per network)
network_mats <- interactions %>%
select(Network_id, Plant_accepted_name, Pollinator_accepted_name, present) %>%
distinct() %>%
pivot_wider(
names_from = Pollinator_accepted_name,
values_from = present,
values_fill = 0
) %>%
split(.$Network_id)
# Convert each to matrix
network_matrices <- lapply(network_mats, function(df) {
mat <- as.matrix(df[,-1])
rownames(mat) <- df$Plant_accepted_name
mat
})
# # calculating the indexes for each network
# network_stats <- lapply(network_matrices, function(m) {
# m_bin <- (m > 0) * 1
# data.frame(
# Connectance = networklevel(m_bin, index = "connectance"),
# Nestedness = networklevel(m_bin, index = "nestedness")
# # H2 = networklevel(m_bin, index = "H2")
# )
# }) %>% bind_rows(.id = "Network_id")
#
# # box plot for the connectance
# network_stats_full <- network_stats %>%
# left_join(interactions %>% distinct(Network_id, Country, Bioregion, EuPPollNet_habitat), by = "Network_id")
# ggplot(network_stats_full, aes(x = Country, y = Connectance)) +
# geom_boxplot(fill = "lightgreen") +
# theme_minimal() +
# labs(title = "Connectance Across Countries", y = "Connectance", x = "Country") +
# theme(axis.text.x = element_text(angle = 45, hjust = 1))
#
# # box plot for the nestedness
# ggplot(network_stats_full, aes(x = Country, y = Nestedness)) +
# geom_boxplot(fill = "salmon") +
# theme_minimal() +
# labs(title = "Nestedness Across Countries", y = "Nestedness", x = "Country") +
# theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Set up parallel backend
cores <- detectCores() - 1
registerDoParallel(cores)
# Step 1: Get network sizes to filter small networks
network_sizes <- lapply(names(network_matrices), function(net_id) {
m <- network_matrices[[net_id]]
data.frame(Network_id = net_id, N_plants = nrow(m), N_pollinators = ncol(m))
}) %>% bind_rows()
# Filter large networks (e.g., >=3 plants and >=3 pollinators)
large_networks <- network_sizes %>%
filter(N_plants >= 3, N_pollinators >= 3) %>%
pull(Network_id)
# Step 2: Calculate network metrics for large networks
network_stats_large <- foreach(net_id = large_networks, .combine = rbind,
.packages = c("igraph", "bipartite")) %dopar% {
m_bin <- (network_matrices[[net_id]] > 0) * 1 # Binary matrix
g <- graph_from_incidence_matrix(m_bin, directed = FALSE)
g_poll <- bipartite.projection(g)$proj2 # Pollinator projection
# Network metrics
net_levels <- networklevel(m_bin, index = c("connectance", "NODF"))
connectance <- net_levels["connectance"]
nodf <- net_levels["NODF"]
evenness <- networklevel(m_bin, index = "interaction evenness")
# Modularity (skip if projected network too small)
mod <- if (vcount(g_poll) >= 5 && ecount(g_poll) >= 5) {
comm <- cluster_fast_greedy(g_poll)
modularity(g_poll, membership(comm))
} else {
NA
}
data.frame(
Network_id = net_id, # Defined within the loop
Connectance = connectance,
Nestedness_NODF = nodf,
Modularity = mod,
Interaction_Evenness = evenness
)
}
# Stop parallel backend
stopImplicitCluster()
# Step 3: Assign NA to small networks
small_networks <- setdiff(names(network_matrices), large_networks)
network_stats_small <- data.frame(
Network_id = small_networks,
Connectance = NA,
Nestedness_NODF = NA,
Modularity = NA,
Interaction_Evenness = NA
)
# Combine results
network_stats <- bind_rows(network_stats_large, network_stats_small)
# Join with metadata
network_stats_full <- network_stats %>%
left_join(interactions %>% distinct(Network_id, Country, Bioregion, EuPPollNet_habitat), by = "Network_id") %>%
left_join(network_sizes, by = "Network_id")
# Visualizations
# Connectance
ggplot(network_stats_full, aes(x = Country, y = Connectance)) +
geom_boxplot(fill = "lightgreen") +
theme_minimal() +
labs(title = "Connectance Across Countries", y = "Connectance", x = "Country") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
## Warning: Removed 165 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

# Nestedness NODF
ggplot(network_stats_full, aes(x = Country, y = Nestedness_NODF)) +
geom_boxplot(fill = "salmon") +
theme_minimal() +
labs(title = "Nestedness (NODF) Across Countries", y = "NODF", x = "Country") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
## Warning: Removed 165 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

# Modularity
ggplot(network_stats_full %>% filter(!is.na(Modularity)), aes(x = Country, y = Modularity)) +
geom_boxplot(fill = "lightpink") +
theme_minimal() +
labs(title = "Modularity Across Countries (Large Networks Only)", y = "Modularity", x = "Country") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))

# Interaction Evenness
ggplot(network_stats_full, aes(x = Country, y = Interaction_Evenness)) +
geom_boxplot(fill = "lightblue") +
theme_minimal() +
labs(title = "Interaction Evenness Across Countries", y = "Evenness", x = "Country") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
## Warning: Removed 165 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

# Summary
cat("Number of small networks (skipped):", nrow(network_stats_small), "\n")
## Number of small networks (skipped): 165
cat("Number of large networks analyzed:", nrow(network_stats_large), "\n")
## Number of large networks analyzed: 1357
summary(network_stats_full[, c("Connectance", "Nestedness_NODF", "Modularity", "Interaction_Evenness")])
## Connectance Nestedness_NODF Modularity Interaction_Evenness
## Min. :0.02549 Min. : 9.774 Min. :-0.10000 Min. :0.6301
## 1st Qu.:0.14264 1st Qu.:25.645 1st Qu.: 0.07124 1st Qu.:0.6800
## Median :0.23810 Median :33.333 Median : 0.16320 Median :0.7099
## Mean :0.25456 Mean :36.259 Mean : 0.15915 Mean :0.7173
## 3rd Qu.:0.34807 3rd Qu.:44.834 3rd Qu.: 0.24097 3rd Qu.:0.7467
## Max. :0.77778 Max. :78.089 Max. : 0.53539 Max. :0.8856
## NA's :165 NA's :165 NA's :213 NA's :165
# Step 1: Aggregate coordinates by Network_id
network_coords <- interactions %>%
group_by(Network_id) %>%
summarise(Latitude = mean(Latitude, na.rm = TRUE),
Longitude = mean(Longitude, na.rm = TRUE)) %>%
left_join(network_stats_full, by = "Network_id")
# Step 2: Get a European map
europe_map <- ne_countries(scale = "medium", continent = "Europe", returnclass = "sf")
# Step 3: Create a spatial plot (e.g., Modularity by location)
ggplot(data = europe_map) +
geom_sf(fill = "lightgray", color = "white") +
geom_point(data = network_coords,
aes(x = Longitude, y = Latitude, color = Modularity),
size = 2, alpha = 0.6) +
scale_color_gradient(low = "blue", high = "red", na.value = "gray",
name = "Modularity") +
coord_sf(xlim = c(-10, 35), ylim = c(35, 72)) +
theme_minimal() +
labs(title = "Modularity Across European Plant-Pollinator Networks",
x = "Longitude", y = "Latitude") +
theme(legend.position = "right")

# Repeat for other metrics (e.g., Interaction_Evenness)
ggplot(data = europe_map) +
geom_sf(fill = "lightgray", color = "white") +
geom_point(data = network_coords,
aes(x = Longitude, y = Latitude, color = Interaction_Evenness),
size = 2, alpha = 0.6) +
scale_color_gradient(low = "blue", high = "green", na.value = "gray",
name = "Evenness") +
coord_sf(xlim = c(-10, 35), ylim = c(35, 72)) +
theme_minimal() +
labs(title = "Interaction Evenness Across European Networks",
x = "Longitude", y = "Latitude") +
theme(legend.position = "right")

# Step 2: Extract coordinates for distance calculation
coords <- network_coords %>%
select(Network_id, Latitude, Longitude) %>%
distinct()
# Convert to matrix of coordinates
coord_matrix <- as.matrix(coords[, c("Longitude", "Latitude")]) # Order: lon, lat
# Step 3: Calculate pairwise distances (in kilometers) using Haversine
dist_matrix <- distm(coord_matrix, fun = distHaversine) / 1000 # Convert meters to km
rownames(dist_matrix) <- coords$Network_id
colnames(dist_matrix) <- coords$Network_id
# Step 4: Convert to long format for easier analysis
dist_long <- as.data.frame(as.table(dist_matrix)) %>%
filter(!is.na(Freq)) %>%
rename(Network1 = Var1, Network2 = Var2, Distance_km = Freq) %>%
filter(Network1 != Network2)
# # Step 5: Summary statistics
# summary_stats <- dist_long %>%
# summarise(
# Min_Distance = min(Distance_km),
# Mean_Distance = mean(Distance_km),
# Max_Distance = max(Distance_km)
# )
# print(summary_stats)
#
# # Example: Find nearest neighbor
# nearest_neighbor <- dist_long %>%
# group_by(Network1) %>%
# slice_min(Distance_km, n = 1) %>%
# rename(Nearest_Network = Network2, Nearest_Distance_km = Distance_km)
# network_coords <- network_coords %>%
# left_join(nearest_neighbor, by = c("Network_id" = "Network1"))
#
# # Optional Visualization: Map with distances
# ggplot(data = europe_map) +
# geom_sf(fill = "lightgray", color = "white") +
# geom_point(data = network_coords, aes(x = Longitude, y = Latitude, color = Nearest_Distance_km), size = 2, alpha = 0.6) +
# scale_color_gradient(low = "blue", high = "red", na.value = "gray", name = "Nearest Distance (km)") +
# coord_sf(xlim = c(-10, 35), ylim = c(35, 72)) +
# theme_minimal() +
# labs(title = "Nearest Neighbor Distances Across Networks",
# x = "Longitude", y = "Latitude") +
# theme(legend.position = "right")
# Spatial plot zoomed on Ireland
ggplot(data = europe_map) +
geom_sf(fill = "lightgray", color = "white") +
geom_point(data = network_coords,
aes(x = Longitude, y = Latitude),
size = 2, alpha = 0.6) +
coord_sf(xlim = c(-10, -5), ylim = c(51, 55)) +
theme_minimal() +
labs(title = " Networks in Ireland",
x = "Longitude", y = "Latitude") +
theme(legend.position = "right")

# Spatial plot zoomed on Germany
ggplot(data = europe_map) +
geom_sf(fill = "lightgray", color = "white") +
geom_point(data = network_coords,
aes(x = Longitude, y = Latitude),
size = 2, alpha = 0.6) +
coord_sf(xlim = c(5, 15), ylim = c(47, 55)) + # Zoom to Germany
theme_minimal() +
labs(title = "Networks in Germany",
x = "Longitude", y = "Latitude") +
theme(legend.position = "right")

# Species-level analysis - degree distribution
species_roles <- lapply(network_matrices, function(m) {
m_bin <- (m > 0) * 1
roles <- specieslevel(m_bin, index = c("degree", "normalized degree"))
# Combine plant + pollinator into one dataframe
df <- bind_rows(
as.data.frame(roles$`higher level`) %>%
rownames_to_column("Species") %>%
mutate(Level = "Plant"),
as.data.frame(roles$`lower level`) %>%
rownames_to_column("Species") %>%
mutate(Level = "Pollinator")
)
df
}) %>%
bind_rows(.id = "Network_id")
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## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
## Warning: Index 'normalized degree' not recognised and hence not computed!
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# # Diagnose: which networks have >1 metadata row?
# interactions %>%
# distinct(Network_id, Country, Bioregion, EuPPollNet_habitat) %>%
# count(Network_id, name = "n_meta_rows") %>%
# filter(n_meta_rows > 1)
# Majority Country per network
country_mode <- network_summary %>%
count(Network_id, Country, name = "n") %>%
group_by(Network_id) %>%
slice_max(n, with_ties = FALSE) %>%
ungroup() %>%
select(Network_id, Country)
# Majority Bioregion per network
bioregion_mode <- network_summary %>%
count(Network_id, Bioregion, name = "n") %>%
group_by(Network_id) %>%
slice_max(n, with_ties = FALSE) %>%
ungroup() %>%
select(Network_id, Bioregion)
# Majority Habitat per network
habitat_mode <- network_summary %>%
count(Network_id, EuPPollNet_habitat, name = "n") %>%
group_by(Network_id) %>%
slice_max(n, with_ties = FALSE) %>%
ungroup() %>%
select(Network_id, EuPPollNet_habitat)
# Combine into one-row-per-network metadata
meta_by_net <- country_mode %>%
left_join(bioregion_mode, by = "Network_id") %>%
left_join(habitat_mode, by = "Network_id")
# Safe join
species_roles_full <- species_roles %>%
left_join(meta_by_net, by = "Network_id")
# Join with metadata
species_roles_full <- species_roles %>%
left_join(interactions %>%
distinct(Network_id, Country, Bioregion, EuPPollNet_habitat),
by = "Network_id")
## Warning in left_join(., interactions %>% distinct(Network_id, Country, Bioregion, : Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 582 of `x` matches multiple rows in `y`.
## ℹ Row 836 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
## "many-to-many"` to silence this warning.
# Explore top high degree
top_generalists <- species_roles_full %>%
arrange(desc(degree)) %>%
group_by(Level) %>%
slice_head(n = 10)
print(top_generalists)
## # A tibble: 20 × 7
## # Groups: Level [2]
## Network_id Species degree Level Country Bioregion EuPPollNet_habitat
## <chr> <chr> <dbl> <chr> <chr> <chr> <chr>
## 1 1 Plant_accepted_… 130 Plant Spain Atlantic Semi-natural gras…
## 2 1 Plant_accepted_… 130 Plant Germany Continen… Agricultural marg…
## 3 1 Plant_accepted_… 130 Plant Germany Continen… Agricultural land
## 4 1 Plant_accepted_… 130 Plant Germany Continen… Forest/woodland
## 5 1 Plant_accepted_… 130 Plant Switze… Continen… Intensive grassla…
## 6 1 Plant_accepted_… 130 Plant Germany Alpine Montane to alpine…
## 7 1 Plant_accepted_… 130 Plant Czech … Continen… Intensive grassla…
## 8 5 Plant_accepted_… 130 Plant Spain Atlantic Semi-natural gras…
## 9 5 Plant_accepted_… 130 Plant Germany Continen… Agricultural marg…
## 10 5 Plant_accepted_… 130 Plant Germany Continen… Agricultural land
## 11 3 Ranunculus acris 84 Poll… Spain Atlantic Semi-natural gras…
## 12 3 Ranunculus acris 84 Poll… Germany Continen… Agricultural marg…
## 13 3 Ranunculus acris 84 Poll… Germany Continen… Agricultural land
## 14 3 Ranunculus acris 84 Poll… Germany Continen… Intensive grassla…
## 15 3 Ranunculus acris 84 Poll… Switze… Continen… Intensive grassla…
## 16 3 Ranunculus acris 84 Poll… Germany Alpine Montane to alpine…
## 17 3 Ranunculus acris 84 Poll… Czech … Continen… Semi-natural gras…
## 18 2 Ranunculus acris 69 Poll… Spain Atlantic Semi-natural gras…
## 19 2 Ranunculus acris 69 Poll… Germany Continen… Agricultural marg…
## 20 2 Ranunculus acris 69 Poll… Germany Continen… Agricultural land
# print(top_specialists)
# Plots
ggplot(species_roles_full, aes(x = degree, fill = Level)) +
geom_histogram(bins = 30, alpha = 0.6, position = "identity") +
theme_minimal() +
labs(title = "Degree distribution of plants and pollinators",
x = "Degree", y = "Number of species")
